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arXiv · 2002.09475

Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence

Andras Szabo·Bitan Roy
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Abstract

We analyze the stability of time-reversal (${\mathcal T}$) and lattice four-fold ($C_4$) symmetry breaking three-dimensional higher-order topological (HOT) Dirac semimetals (DSMs) and the associated one-dimensional hinge modes in the presence of random pointlike charge impurities. Complementary real space numerical and momentum space renormalization group (RG) analyses suggest that a HOTDSM, while being a stable phase of matter for sufficiently weak disorder, undergoes a continuous quantum phase transition into a trivial metal at finite disorder. However, the corresponding critical exponents (numerically obtained from the scaling of the density of states) are extremely close to the ones found in a dirty, but first-order DSM that on the other hand preserves ${\mathcal T}$ and $C_4$ symmetries, and support two Fermi arc surface states. This observation suggests an emergent \emph{superuniversality} (insensitive to symmetries) in the entire family of dirty DSMs, as also predicted by a leading-order RG analysis. As a direct consequence of the bulk-boundary correspondence, the hinge modes in a system with open boundaries gradually fade away with increasing randomness, and completely dissolve in the trivial metallic phase at strong disorder.

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Andras Szabo, Bitan Roy. 2020-02-21. Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence. https://doi.org/10.1103/physrevresearch.2.043197

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